Theresa May today signalled a new push to tackle extremism by challenging its "bigoted ideology" head on and prosecuting those who support attacks on civilians "anywhere in the world".

The home secretary told the Tory conference in Birmingham she was turning Labour's "failed" approach of locking people up for 90 days without charge, introducing ID cards and "engaging with extremists" on its head.

May said the review of counter-terrorism laws would ensure the ideology fuelling the terror threat faced by Britain was challenged.

The home secretary also made it clear that the government would now only work with "moderate voices" and would end the practice of "engaging with extremists".

"Foreign hate preachers will no longer be welcome here," she said. "Those who step outside the law to incite hatred and violence will be prosecuted and punished.

"And we will stand up to anybody who incites hatred and violence, who supports attacks on British troops, or who supports attacks on civilians anywhere in the world."

May's speech reflects progress in the current Home Office review of the counter-terrorism laws, which is also examining the option of banning organisations that incite hatred or violence on the advice of the security services.

The home secretary also said she intended to introduce a new sanctions regime to deal with antisocial behaviour to replace the current "alphabet soup" of "Isos, Abcs, Asbis, Asbos and Crasbos".

She confirmed that victims who failed to get a police response to repeated complaints of antisocial behaviour would get a new right to force them to take action.

Her speech followed one by the justice secretary, Ken Clarke, who was cheered several times – albeit by a half-empty hall – as he revealed details of his plan for a major expansion of prison industries to get most prisoners working a full, 40-hour week in public sector prisons.

He also confirmed that the government will change the law to use part of the revenue raised by paying inmates the national minimum wage to support victims' funds.

But for Clarke – already under tabloid attack for his plans to address the rise in the prison population – the prison work plan was a kind of "iron glove in a velvet fist".

He said it was important to recognise that prisons were not only filled with muggers, burglars and violent and dangerous individuals.

Jails also contained "thousands of antisocial, petty criminals who fail to behave themselves in everyday life", almost half of them illiterate, mentally ill or with a history of drug abuse.

"I've never been in favour of mollycoddling criminals," Clarke said, before adding that the criminal justice system really had to do better than that.

He announced plans for new "drug-free wings" in prisons and said he hoped the government's sentencing review would produce tougher community punishments that proved as effective as those in France and Germany at cutting reoffending.

He also highlighted the introduction of the first "payment by results" scheme being introduced to cut the reoffending rates of short-term prisoners.

"I have visited the Peterborough Project and I've seen how it can work. I'm an enthusiast. So I can tell you today that we will be starting up a range of similar schemes in England and Wales in the new year," he said.

"We will look at bids from serious groups who want to take whatever approach they believe in – from boot camps to more therapeutic options. And the taxpayer will pay for what works and what cuts crime."